I am going to say maybe juicing isn't a good idea with low carb... The fiber in fruits and veggies is good and slows down digestion so you don't have a spike in blood sugar.
trying searching fawn and her green smoothie

I just ordered a new juicer for myself for Valentine's Day (it is red )

I had one before and just stuck to mostly green vegetables. Most of the recipes call for a lot of fruit so you'll have to figure it out for yourself mostly.

Cucumber makes a good base (peel first) and has lots of juice. I add spinach or other leafy dark greens for the vitamins. A little lemon makes for good flavor. Carrots are good, but fairly sweet so go easy. Celery is also good.

It isn't strictly low carb, but juicing has it's own benefits. Try it and see if it works for you.